Weakly Semiprime Segments in Ordered Semigroups

Mathematics

Thawhat Changphas¹  Panuwat Luangchaisri¹ 

[1] Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand;

关键词: weakly semiprime;    prime;    segment;    ordered semigroup;   

DOI  :  10.3390/math7090800

来源: DOAJ

【 摘 要 】

Let $P_2\subset P_1$ be a pair of weakly semiprime ideals of an ordered semigroup $(S,·,\le )$ . Then, the pair $P_2\subset P_1$ is called a weakly semiprime segment of S if ${\bigcap }_{n\in \mathbb{N}}{I}^n\subseteq P_2$ for all ideals I of S such that $P_2\subset I\subset P_1$ . In this paper, we classify weakly semiprime segments of an ordered semigroup into four types; those that are simple, exceptional, Archimedean, and decomposable.

【 授权许可】

Unknown